The behavior of a system is commonly characterized by stimulating the system with a step input and then measuring the resulting transient response of the system, also referred to as the “step response.” For example, a phase-locked loop (PLL) can be characterized by programming the PLL to step or “hop” from a first frequency to a second frequency and then measuring the resulting transient response of the PLL. For more information on step response measurements, see the book “Modern Control Engineering” by Katsuhiko Ogata, fifth edition, Prentice Hall, 2009.
Test and measurement instruments such as real-time spectrum analyzers, vector signal analyzers, and oscilloscopes are typically used to measure the transient response of a PLL. These test and measurement instruments digitize the output signal of the PLL and then process it to provide a display of the instantaneous frequency of the output signal as shown in FIG. 1, also referred to as the “frequency step response.” Some test and measurement instruments also provide various measurements of the frequency step response such as delay time, rise time, peak time, maximum overshoot, mean settled value, settling time, and so on. Settling time, which indicates how quickly the output signal settles to the second frequency, is of particular interest to users because it has a direct impact on how much data the PLL is able to transmit between each hop. For more information on characterizing phase-locked loops using test and measurement instruments, see Tektronix document number 37W-18170 titled “Characterizing Phase Locked Loops Using Tektronix Real-Time Spectrum Analyzers” available at http://www.tek.com/.
Increasingly, in addition to needing to measure how quickly the output signal settles to the second frequency, users also need to measure how quickly the output signal settles to a stable phase, also referred to as “phase settling time.” Some test and measurement instruments can process the output signal of the PLL to provide a display of the instantaneous phase of the output signal as shown in FIG. 2, also referred to as the “phase transient response.” However, it is difficult to measure the phase settling time based on such a phase transient response because the instantaneous phase accumulates and wraps so rapidly, thereby masking subtle phase settling behavior.
In order to reveal the subtle phase settling behavior, some test and measurement instruments process the phase transient response to provide a “flattened” phase transient response as shown in FIG. 3. However, in order to do so, all of these test and measurement instruments require that the user intervene in some way. Some test and measurement instruments require that the user manually enter the second frequency value. Other test and measurement instruments require that the user manually specify points on the phase transient response where the user believes that the phase transient response has settled to a stable phase. In either case, requiring user intervention is time-consuming and inconvenient for the user.
What is needed is a method of measuring the phase transient response of a system under test that does not require any user intervention.